MEP-Technical Manual CDN 0408.qxd - Hambro

DESIGN PRINCIPLES AND CALCULATIONS
4.6 DIAPHRAGM DESIGN
4.6.1 THE HAMBRO SLAB AS A DIAPHRAGM
With the increasing use of the Hambro system for floor of
buildings in earthquake prone areas such as Anchorage,
Los Angeles, Vancouver, Montreal and Quebec City or in
hurricane prone areas such as Florida as well as for multistorey
buildings where shear transfer could occur at some
level of the building due to the reduction of the floor plan,
it is important to develop an understanding of how the
slabs will be able to transmit horizontal loads while being
part of the Hambro floor system.
The floor slab, part of the Hambro system, must be designed
by the project structural engineer as a diaphragm to resist
horizontal loads and transmit them to the vertical bracing
system.
Any diaphragm has the following limit states:
1) Shear strength between the supports
2) Out of plane buckling
3) In plane deflection of the diaphragm
4) Shear transmission at the supports
A diaphragm works as the web of a beam spanning
between or extending beyond the supports. In the case of
a floor slab, the slab is the web of the beam spanning
between or extending beyond the vertical elements
designed to transmit to the foundations the horizontal
loads produced by earthquake or wind.
We will use a simple example of wind load acting on a
diaphragm part of a horizontal beam forming a single span
between end walls. The structural engineer responsible for
the design of the building shall establish the horizontal
loads that must be resisted at each floor of the building for
the wind and earthquake conditions prevailing at the building
location. The structural engineer must also identify the
vertical elements that will transmit the horizontal loads to
the foundations in order to calculate the shear that must be
resisted by the floor slab.
4.6.2 SHEAR STRENGTH BETWEEN SUPPORTS
A series of fourteen specimens of concrete slabs, part of a
Hambro floor system, were tested in the laboratories of
Carleton University in Ottawa. The purpose of the tests was
to identify the variables affecting the in plane shear strength
of the concrete slab reinforced with welded wire mesh.
The specimens were made of slabs with a concrete thickness
of 63 mm (2.5”) or 70 mm (2.75”) forming a beam with
a span of 610 mm (24”) and a depth of 610 mm (24”). This
beam was loaded with two equal concentrated loads at
152 mm (6”) from the supports. The other variables were:
1) The size of the wire mesh
2) The presence or absence of the Hambro joist embedded
top chord parallel to the load in the shear zone
3) The concrete strength
It was found that the shear resistance of the slab is minimized
when the shear stress is parallel to the Hambro joist
embedded top chord. A conservative assumption could be
made that the concrete confined steel wire mesh is the
only element that will transmit the shear load over the
embedded top chord.
In the following example of the design procedure, we will
take into account that the steel of the wire mesh is already
under tension stresses produced by the continuity of the
slab over the Hambro joist, and that the remaining
capacity of the steel wire mesh will be the limiting factor
for the shear strength of the slab.
The largest bending moment is over the embedded
top chord and is calculated for one meter width. In using
the example from section 4.1.5 page 5, the non factored
moment is:
Dead load*: Mfd = 3KPa x (1.2m) 2 / 10 = 0.43 kN•m
Live load*: MfL = 2KPa x (1.2m) 2 / 10 = 0.29 kN•m.
1) Loads
Factored dead load: 1.25 x 3.0 = 3.75 kPa
Factored live load: 1.50 x 2.0 = 3.00 kPa
Factored total load: 6.75 kPa
And thus the factored live load accounts for 44% of the
factored total load.
2) Bending moment in the slab between joists due to
gravity loads
The smallest lever arm between the compression concrete
surface and the tension steel of the wire mesh is also over
the embedded top chord. This dimension allows us to
calculate the factored bending capacity of the slab to be
Mr = 1.61 kN•m*.
To establish the shear capacity of steel wire mesh for a slab
unit width of one meter, we use the following formula
adapted from CSA A23.3-04 clause 11.5 and simplified
to calculate the resistance of the reinforcing steel only,
considering a shear crack developing at a 45 degree angle
and intersecting the wire mesh in both directions.
V r = ø s x A s x F y x cos (45°)
= 0.85 x 2 x 123 x 400 x 0.707/1 000
= 59.1 kN for a meter width of slab
* See page 5 for calculation.
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